The toy manufacturer's overall daily demand is assumed to be linear and contingent upon the pricing of toys: D=100015p. The unit cost of each toy is $3, and the manufacturer also pays a daily rental of $100. a) What is the manufacturer's revenue if the selling price is $80 ? b) What is the optimal selling price that maximizes the manufacturer's revenue? c) The manufacturer wants to create customer segments by determining 3 different selling prices. Specifically, the manufacturer will sell the first Q1 amount of toys at the price of p1, the second Q2 at the price of p2, and finally, the last Q3 toys at p3, where p3>p2>p1. Write down the equations for Q1,Q2, and Q3, and build a mathematical model that will maximize the - manufacturer's revenue. d) A new toy supplier enters the market and wants to buy toys in bulk. The supplier's daily demand is estimated to be 1l2025p. Due to increasing market potential, the manufacturer must now take into account her daily production capacity of 800 . How would you update the mathematical formulation from part c, if the manufacturer wants to sell the toys to the supplier using the price of p4